Proceedings PaperOptimum Undulator Trajectories
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The undulator is a machine that induces amplitude fluctuations in normally-rectilinear electron trajectories, causing coherently-reinforced radiation to appear along the direction of electron motion. Presently, such machines operate on electrons travelling in straight sections of synchrotron rings. The inherently large number of variables characterizing the undulator-electron interaction makes it difficult to identify the principal parameters for c-)t-Lmization when designing synchrotron rings dedicated to undulator operation. In this paper we present the results of a variational analysis of the equation describing undulator radiation. In particular, our results identify the optimum electron trajec-tories in undulators, in the sense of maximizing the intensity of the emitted radiation in the forward direction, and establish the optimum amplitudes of the electron motion. These important results are presented in terms of the total electron velocity, 13c, and the average on-axis velocity 3*c. The results, besides providing a valuable insight into undulator operation, rigorously establish the principal optimization parameters for associated syn-chrontron ring design.